Definition:Proper Subset/Proper Superset
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Definition
If $S$ is a proper subset of $T$, then $T$ is a proper superset of $S$.
This can be expressed by the notation $T \supsetneqq S$.
Also known as
$S \subsetneqq T$ can also be read as:
- $S$ is properly included in $T$, or $T$ properly includes $S$
- $S$ is strictly included in $T$, or $T$ strictly includes $S$
The following usage can also be seen for $S \subsetneqq T$:
- $S$ is properly contained in $T$, or $T$ properly contains $S$
- $S$ is strictly contained in $T$, or $T$ strictly contains $S$
However, beware of the usage of contains: $S$ contains $T$ can also be interpreted as $S$ is an element of $T$.
Hence the use of contains is not supported on $\mathsf{Pr} \infty \mathsf{fWiki}$.
Sources
- 1963: George F. Simmons: Introduction to Topology and Modern Analysis ... (previous) ... (next): $\S 1$: Sets and Set Inclusion
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {III}$: The Natural Numbers: $\S 17$: Finite Sets